Two blocks $A$ and $B$ of masses $6 \, kg$ and $3 \, kg$ rest on a smooth horizontal surface as shown in the figure. If the coefficient of friction between $A$ and $B$ is $0.4$,find the maximum horizontal force $F$ that can be applied to block $A$ such that they move together without separation. (in $, N$)

As shown in the figure, block $m$ and wedge $M$ move together with a horizontal acceleration of $20\, m/s^2$. Given $m = 1\, kg$, $\mu = 0.6$ (between $m$ and $M$) and $g = 10\, m/s^2$. Choose the $\text{CORRECT}$ alternative:

The system shown in the figure is released. Find the accelerations $a_1$ (for the $2 \ kg$ block) and $a_2$ (for the $3 \ kg$ block).

$A$ block of mass $m_{2}$ is placed on a horizontal table and another block of mass $m_{1}$ is placed on top of it. An increasing horizontal force $F=\alpha t$ is exerted on the upper block, but the lower block never moves as a result. If the coefficient of friction between the blocks is $\mu_{1}$ and that between the lower block and the table is $\mu_{2}$, then what is the maximum possible value of $\mu_{1} / \mu_{2}$?

If $100 \,N$ force is applied to $10 \,kg$ block as shown in the diagram,the acceleration of $40 \,kg$ slab is (in $\,ms^{-2}$)

When $F = 2 \text{ N}$, what is the frictional force between the $5 \text{ kg}$ block and the ground (in $\text{ N}$)?